


Touching

by Bitenomnom



Series: Mathematical Proof [9]
Category: Sherlock (TV)
Genre: Character Death, Love, M/M, Mathematics, Past Relationship(s), Pining, Reunion, Separation, Sherlock and John are exes, Twenty Years Later
Language: English
Status: Completed
Published: 2012-09-18
Updated: 2012-09-18
Packaged: 2017-11-14 12:32:15
Rating: Not Rated
Warnings: Creator Chose Not To Use Archive Warnings
Chapters: 1
Words: 3,111
Publisher: archiveofourown.org
Story URL: https://archiveofourown.org/works/515273
Author URL: https://archiveofourown.org/users/Bitenomnom/pseuds/Bitenomnom
Summary: <blockquote class="userstuff">
              <p>He and John fell in love eighteen years ago.</p><p>It fell apart quickly.<br/>It fell apart suddenly.<br/>It fell apart sixteen years ago.</p><p>But they were still flatmates, and they still solved crimes, and nothing changed. Nothing changed sixteen years ago, just the details, just the important little details. Sherlock was no longer allowed to sleep in bed with John, or run his fingers through John’s hair or breathe on his collarbone or nip at his nose or sleep with his face buried in a discarded jumper or lay his head in John’s lap while they watched John’s action and sci-fi movies.</p><p>Everything changed fourteen years ago, though. <i>Everything.</i></p>
            </blockquote>





	Touching

**Author's Note:**

> Okay, okay! I confess! This one is stretching the limits of the "however vaguely" in "however vaguely related to my classes." The thing is, I actually had five other topics I was going to choose from, and then, like, two minutes before the end of class, the prof said something and the phrase sparked an idea and I was inspired and had to run with it. To make up for that, I tried to include an extra-thorough description of the math we were working on up to that point. The bit that inspired this is at the end of the math section, but in case you're for some reason in the habit of skipping that section, the gist is that when talking about two variables, x1 and x2, interacting, he described it as "the x's are touching." Which I naturally heard as "exes" and there you go.
> 
> So the math bit of this covers several of the topics I was thinking about covering. And then the writing part basically contains no math (maybe some basic addition and subtraction). Only touching exes. (But no, not smutty, sorry. It's 4am and I don't have all the time in the world.)

In gathering and analyzing data, one may find that some of the data is qualitative in nature. (For instance, some data collected may be sex, country of origin, type of profession, and so on.) This data may be just as important as any of the numerical data gathered, so we must devise a way to include it in our analysis. We may find that the y-intercept of our linear regression varies, for instance, for different categories. In that case, we create a “dummy” or “indicator” variable to take the place of the qualitative data. In analyzing a set of data, for instance, where surveyed persons were recorded as “male” or “female,” one can create a dummy variable that takes on the value 0 for males and 1 for females. In doing so, we essentially generate two lines with equal slopes: one with an intercept corresponding to the “male” data, and one with an intercept corresponding to the “female” data.

 

We may also find that the slope of our data varies from category to category. (This may manifest itself as a lack of constant variance when all data is viewed at once, without considering the differences between the qualitative variables.) We can similarly create one or more dummy variables to switch “on” or “off” depending on the category. This time, these dummy variables are multiplied to the “X” values of our data. Take our “male/female” example and say we believe the slopes of the lines might vary based on sex. We can use the same rule of 0 for male, 1 for female, and get this “baseline” equation for males:  
  
Y = α + β1x1 \+ ε

 

Where α is the intercept, β1 is the slope, and ε is the error. We may wish to express the slope of the “female” line as a comparison to that of the “male” line (using it as a baseline), and also consider the possibility that this line has a different intercept. So we can write

 

Y = α + β2 \+ (β1 \+ β3)x1 \+ ε

 

Here, β2 is the possible change in intercept value from that of the “male” line, and β3 is the possible change in slope from that of the “male” line. But we need to combine the two into one equation that will help us sort out the males and females, so we create a dummy variable as we did before; call it x2 (0 for males, 1 for females). Then we have

 

Y = α + β1x1 \+ β2x2 \+ β3x1 x2 \+ ε

 

We have our x2 variable to switch the β2 and β3 “off” if the data point is in the “male” (0 or “off”) category. The fact that there are x’s multiplied together does not mean that the regression is not linear; while it is not linear in the x’s, it is linear in our parameters, which is what we refer to by the phrase “linear model.” The fact that there are some x’s multiplied together in some terms means there is “interaction” between the x’s.

 

Or to quote my professor, “Before, the x’s never touched each other. Now we have some touching going on.”

 

***

 

            Six years had passed.

            No, sixteen.

            Well, there was a reason Sherlock generally left the mathematics to someone else.

            Sixteen years ago, nothing had changed. He and John continued being flatmates. He and John solved crimes. He and John took back London, took back Sherlock’s name from Moriarty’s clutches after Sherlock came back to life and then some, because that was long done before sixteen years ago. He and John. He and John.

            He and John fell in love. Eight—eighteen years ago.

            There was no other word for it and Sherlock saw little point in rejecting the idea when everyone insisted, when Lestrade insisted that yes, _yes,_ that thing he was feeling about John was _love_ and a particular type, _romantic_ love, hearts-and-roses. John, bless John, did bring him roses once. It wasn’t all roses; it was gruesome, too, and gritty, and John knew it, and embraced it, and it was _right_. Sherlock came to life and John came to life, a matching pair, and everyone _saw_ and everyone _knew_ and life flurried on around them just about the same as before but with hand-holding and kisses stolen in the entry to 221. Sherlock had even tried sex, and loved that too, because all sex was was loving John’s body, and Sherlock loved all of John.

            It fell apart quickly.

            It fell apart suddenly.

            It fell apart sixteen years ago.

            Sherlock so sorely wished he had not deleted the details of the case the moment it was over, because the details of the case were the reason it happened, the falling-apart, and he was left unable to analyze what he’d done, unable to understand. Something, it was _something_ , and John could only say, “I’m sorry, Sherlock, it’s too much, I’m sorry, it’s one too many things, I’m sorry, I’m sorry.”

            And he _was_ sorry. And he was so good about it. Whatever Sherlock had done, it was never mentioned again. Nothing was ever mentioned again, except that Sherlock was no longer allowed to sleep in bed with John, or run his fingers through John’s hair or breathe on his collarbone or nip at his nose or sleep with his face buried in a discarded jumper or lay his head in John’s lap while they watched John’s action and sci-fi movies, whichever John wanted, no matter how awful, like everything John fancied that Sherlock had learned to love, somehow, too, as a part of John, just as John had loved the skull and Sherlock’s microscope and the little dances Sherlock did when strange new corpses were found washed up from rivers.

            But everything carried on as usual besides that. They were still flatmates and Sherlock still ran experiments and John still popped in an awful film Saturday nights and they still watched it together and Sherlock still watched John’s eyes as they lit up with joy and laughter, except now it wasn’t so much because of Sherlock as it had been before. Just a little, just a little Sherlock, just Sherlock-his-flatmate, just Sherlock-his-friend. Their friendship was a bit tenser—John hesitated, he did, at the things he wouldn’t have when they first met, at pouring out every ounce of his heart through every part of his body, and it wasn’t _right_ because pouring out every ounce of his heart was what John _did_ and it broke Sherlock’s own heart to watch him pause and hold it in, pause and hold it back.

            But they were still flatmates, and they still solved crimes, and nothing changed. Nothing changed sixteen years ago, just the details, just the important little details.

            Everything changed fourteen years ago, though. _Everything._            

            John disappeared because John loved Mary now in all he ways he used to love Sherlock. John married Mary. Mary wasn’t bad. Mary was an exemplary human being just like John, full of light and love, quick and clever and unpredictable in the same unassuming way John was. Sherlock should have liked Mary more, and he would have, but John loved Mary now in all the ways he used to love Sherlock.

            Their friendship came back. It was something. It was better than it had been, he told himself. Sherlock cupped it between his palms like a firefly and held it close to him at nights, peeking through shifted thumbs to make sure it was still there.

            It was stupid to expect anything other than what happened: John still came to cases. John still ran about London. John asked after Sherlock’s health and made sure he ate whenever he came by and two or three times a year his heart would dribble out through shining eyes and a split-wide mouth and weight shifting with excitement and verve in the cold city air.

            And it was a good thing Sherlock got those, those glimpses of light, new chances to capture them between his palms. Fireflies die. Sherlock went some nights without glowing inside his hands before he could catch one again, and he held less and less light to his chest as time passed and they saw less of each other. Life rotated around him as usual; Lestrade swore he would retire soon; Mycroft visited to make sure Sherlock hadn’t done anything _too_ stupid yet, and because he was a cruel bastard asked how John was holding up these days every time he did; Molly worked elsewhere now, but still came by sometimes, and as always, as usual, knew. Life rotated around Sherlock. He should have been moving too, should have been progressing, but he was not. He did the same things, but alone, like before. He kept off drugs but wondered if John would come back if he didn’t. He knew it was an unhealthy thought.

            He still lived at 221B. Mrs. Hudson did not. Mrs. Hudson had passed on four weeks ago, her memory not what it used to be. Sherlock hadn’t the heart to call John up and tell him she was ill and falling fast, hadn’t the strength for Mrs. Hudson to forget that even after John’s marriage and then his wife’s death to cancer and his subsequent pouring of himself into locum work anywhere it took him, even after all that, after fourteen years, that Sherlock and John did not live together any longer. Most of Mrs. Hudson’s other friends had died before her; Sherlock was the only one to stop by and see her on the day she died. Sherlock held her hand while her breathing slowed. Sherlock let his heart get the better of him again, and wept quietly until her last breath drifted from her body. Forgetfulness or not, Mrs. Hudson knew Sherlock. She knew him exactly as he was until her very end. From the afterlife she would fret over the state of his flat; from the afterlife she would ask why didn’t he call John up and invite him over for tea? Nothing formal, just a chat about the good old days, she’d say, and then see Sherlock’s eyes, and stop.

            Sixteen seconds ago, Sherlock had dialed John’s mobile number in the hopes it hadn’t changed since the last time he saw him, something like three years ago. John could refuse to answer if he wanted; Sherlock hadn’t changed his number. If John still had it in his phone, or still recognized it, he could decide to ignore it.

            “Sherlock? Is something wrong?”

            “No,” Sherlock said quietly. “Nothing like that.” Everything was wrong. Every bone in his body was wrong. Maybe he could find Irene and she would tell him how to make John remember how much they loved each other. Maybe he could find Irene and she would run her hand through his hair so patronizingly that it couldn’t be construed as romantic, with so much practice that it was nothing but a paid service. Maybe Irene was as lonely as he was. Maybe they could hate each other and chase each other and she could ruin him again, and he could ruin her again, and the world would kick back in and get to turning even without John.

            Maybe not.

            “What is it?”

            “Just calling,” Sherlock said, but that wasn’t enough, because John could still hang up now, could still dismiss him. “Mrs. Hudson died last month.”

            “Oh, god,” he said. His voice was older. “Was it bad? Why didn’t you tell me?”

            “An illness. It was sudden,” Sherlock said. “And quick. And she…she didn’t die alone.”

            “You were there?”

            “Yes.”

            “Well, I’m glad someone was. Christ. Mrs. Hudson. How…I mean…did she…”

            “I think she must’ve put half of every one of our rent payments in savings,” Sherlock said, and it was that thought, for some reason, _that_ thought that constricted his throat and reddened his eyes—maybe that or maybe that he had said _our_ without thinking, even though it had been just Sherlock for twice and three times as long as it had ever been Sherlock and John, and John hadn’t corrected him— “She…she left me 221.” He took in a breath that rattled, and he hoped the phone static masked it. “She told me to say ‘hello’ to you. And ‘goodbye.’”

            “For her, I hope, not you,” John said. His voice was quiet, as if he knew that Sherlock had been considering returning to his drug habits of decades ago, as if he knew Sherlock was getting reckless and stupid and forgetting and not because he couldn’t remember but because there wasn’t all that much worth keeping on his hard drive that wasn’t already there.

            “Yes, of course. For her.”

            “I’m glad you were there, Sherlock,” John said. “I really am. And I’d bet if she could’ve had anyone by her bedside, she still would’ve chosen you. I know I…well.”

            “Yes,” Sherlock said, swallowing. “Me too.”

            “So you’re still at 221B, then?” John continued, after nearly a minute’s silence. Sherlock would have thought he’d hung up, except that the call timer on the phone kept running.

            “I am,” Sherlock said.

            “You still got that bloody skull on the mantelpiece?”

            Sherlock took in a breath that stuttered in his throat. “I still have about half of your crap film collection that you never picked up. And I still have a television.”

            He could hear John smiling. “God, you don’t watch television now, do you?”

            “Hardly.” His lips wobbled. “I watch your crap film collection.”

            The other end of the line was silent. The timer continued to run. Two minutes, fifty-three seconds since he had called John.

            “I was wondering where _You Only Live Twice_ went,” John finally said. “Perhaps I’ll come get it back.”

            “I’m not sure I can part with it,” Sherlock said, which was truer than he wanted it to be.

            “And I suppose you couldn’t do without any of the others, either?”

            “Most definitely not.” He took in a deep breath, emboldened by the return of life to their banter. “You shall have to stop by if you want to watch them.”  
            “Oh?”

“Crime in London isn’t what it used to be, so I’m often sitting about. It may be a nice distraction from my latest work on concealable explosives.”

            “Concea— _Sherlock_!”

            “In fact, I ought to get back to that right now. Now that I don’t owe anyone anything if I destroy, say, a wall or two…”

            The timer stopped. Twelve seconds later, his phone beeped.

            _set your sorry arse on the sofa and wait for me to get there – JW_

_DONT TOUCH ANYTHING – JW_

_Excepting, I suppose, the sofa? – SH_

_if you are even thinking about blowing up the sofa –JW_

_Wouldn’t dream of it. – SH_

_But if I do it’ll be your side. –SH_

He heard nothing more from John until the knock at the door twenty-two minutes later.

            “I still have a side, do I?” he asked as Sherlock swung it open. Yes, his voice was older. He was older. They were both older.

            “Always, John,” Sherlock could not entirely repress the return of the twitch in his lips as he struggled to smile like a regular person. John was—John. For all he looked different from the last time Sherlock had seen him, he had some features that stayed constant, that had always stayed constant, some part of him that was simply part of his being John. The cane at his side was not one of them. “What’s this?” Sherlock snatched it away.

            “It’s called a ‘cane,’” John seemed to be attempting to smirk, but nothing could hide the scowl that overcame his features. Sherlock tossed the thing to one side, letting it clatter onto the sidewalk. “That’s littering, Sherlock,” he said, staring after it.

            “I walk on the dangerous side these days,” Sherlock stepped aside, hoping John would take the hint and forget about his cane and come in. John glanced after the cane one more time before shaking his head, smiling to himself, and entering. “Just yesterday I failed to recycle a cardboard box.”

            “Christ,” John’s smile grew wider, “how do you live with yourself?”

            Which, of course, immediately sobered Sherlock’s expression, if only for a second, and John saw it, and the smile dropped off his face as well.

            “I notice you completely ignored my instructions,” John finally said as they made their way to B. “I said to stay on the sofa.”

            “I didn’t blow anything up,” Sherlock pointed out.

            “And I suppose that’s all anyone could really ask for.” John crouched in front of the television set and glanced through the pile of DVDs he’d left. “What do you think? Oh, _Moon,_ I haven’t seen that one in ages.”

            “I watched it last week.”

            “Oh, well, we can—”

            “Nonsense. I can see it again. It’s one of the few _good_ films in your collection.”

            “I’ve changed my mind. Let’s do _Hitchhiker’s Guide._ Haven’t seen that one too recently, have you?”

            He hadn’t. Sherlock avoided that one for the most part; the actor who played the main character reminded him too much of John. But here John was, in Baker Street with him for the first time in years. “Not at all.”

            “Right,” John set it up, and then took a seat on the sofa. “God, I missed this.”

            “Me too,” said Sherlock as the opening credits rolled, settling into his own place. Once they were thirty-four minutes into the movie—far enough that John had committed to it, would have to stay and watch the rest—Sherlock said, “I missed _you_ , John.” When John remained silent, he added, “Please don’t go away.”

            “You know,” said John, “something about this doesn’t quite feel like it should.”

            “I’ve forgotten to tell you to make us tea,” Sherlock offered.

            “No, not that,” John chewed his lip thoughtfully. “Not that…”

            “I may have shifted the sofa away from the wall slightly.”

            “Not that either.”

            “We typically didn’t watch movies together until after seven o’clock and it’s only five fifty-three?”  
            “No,” John shifted his weight and settled in a bit more. “No, none of that’s what’s throwing me. Ah!” he feigned a dramatic realization akin to one of Sherlock’s. “I know.”

            “What?”

            “You haven’t laid your head down on my lap yet.”

            And he did, and John ran his fingers through Sherlock’s hair, and Sherlock breathed on John’s collarbone, and later, they shared a bed, and Sherlock loved John, and John loved Sherlock, and twenty-two years after John moved into Baker Street for the first time, he returned.

**Author's Note:**

> Followed up by a second part, [Interaction](http://archiveofourown.org/works/517933), from John's point of view.


End file.
